A comparative study of regression, neural network and neuro-fuzzy inference system for determining the compressive strength of brick–mortar masonry by fusing nondestructive testing data


Determining the compressive strength of masonry structures is critical for assessing their service life and thus providing safety assurances to their occupants and valued stakeholders. This paper presents a methodology based on various data fusion systems for predicting the compressive strength using data collected from nondestructive testing. According to the experimental readings obtained from the laboratory tests for masonry wallettes, 44 samples are used to construct the training datasets and results validated against a masonry structure located in Kharagpur. The compressive strength of masonry units is predicted using statistical regression models and other state-of-the-art approaches. Two indices, namely the coefficient of determination (\(R^2\)) and root mean square error, are used to test the performance of different models. The results indicate that both neural network and neuro-fuzzy inference system have a superior predictive capacity than other models and can be reliably employed in the field to evaluate the compressive strength of brick–mortar masonry structures.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


  1. 1.

    ICOMOS Charter (2005) Principles for the analysis, conservation and structural restoration of architectural heritage. In: International committee on analysis and restoration of structures of architectural heritage. Recommendations for the analysis and restoration of structures of architectural heritage

  2. 2.

    Lourenço PB, Pina-Henriques J (2006) Validation of analytical and continuum numerical methods for estimating the compressive strength of masonry. Comput Struct 84(29–30):1977–1989

    Google Scholar 

  3. 3.

    Köksal HO, Karakoç C, Yildirim H (2005) Compression behavior and failure mechanisms of concrete masonry prisms. J Mater Civ Eng 17(1):107–115

    Google Scholar 

  4. 4.

    Binda L, Saisi A, Tiraboschi C (2000) Investigation procedures for the diagnosis of historic masonries Constr. Build Mater 14(4):199–233

    Google Scholar 

  5. 5.

    Mishra M, Barman S, Maity D, Maiti DK (2018) Ant lion optimisation algorithm for structural damage detection using vibration data. J Civ Struct Health Monit 9(1):117–136

    Google Scholar 

  6. 6.

    Masi A, Chiauzzi L (2013) An experimental study on the within-member variability of in situ concrete strength in RC building structures. Constr Build Mater 47:951–961

    Google Scholar 

  7. 7.

    Brencich A, Sterpi E (2006) Compressive strength of solid clay brick masonry: calibration of experimental tests and theoretical issues. In: Laurenco PB, Roca P, Modena C, Agrawal S (eds) Structural analysis of historical construction. Macmillan, New Delhi, pp 1–8

    Google Scholar 

  8. 8.

    Bogas JA, Gomes MG, Gomes A (2013) Compressive strength evaluation of structural lightweight concrete by non-destructive ultrasonic pulse velocity method. Ultrasonics 53(5):962–972

    Google Scholar 

  9. 9.

    Sabbağ N, Uyanık O (2017) Prediction of reinforced concrete strength by ultrasonic velocities. J Appl Geophys 141:13–23

    Google Scholar 

  10. 10.

    Gros XE (1996) NDT data fusion. Arnold Publisher, London, pp 1–205

    Google Scholar 

  11. 11.

    McCann M, Forde MC (2011) Review of NDT methods in the assessment of concrete and masonry structures. NDT E Int 34(2):71–84

    Google Scholar 

  12. 12.

    Nguyen NT, Sbartai ZM, Lataste JF, Breysse D, Bos F (2013) Assessing the spatial variability of concrete structures using NDT techniques—laboratory tests and case study. Constr Build Mater 49:240–250

    Google Scholar 

  13. 13.

    IS 1992a IS 13311 (Part II): 1992 Non-destructive testing of concrete—methods of test (Rebound Hammer)

  14. 14.

    IS 1992b IS 13311 (Part I): 1992 non-destructive testing of concrete—methods of test (Ultrasonic Pulse Velocity)

  15. 15.

    Malhotra VM, Carino NJ (1991) Handbook on non-destructive testing of concrete. ASTM, CRC Press, Boca Raton

    Google Scholar 

  16. 16.

    Rilem Report TC43-CND (1983) Draft recommendations for in situ concrete strength determination by combined non-destructive methods. Mater Struct 26(155):43–49

    Google Scholar 

  17. 17.

    Uva G, Porco F, Fiore A (2016) The SonReb method: critical review and practical aspects. In: Proceedings of Italian concrete days, pp 161–171

  18. 18.

    Vasanellia E, Sileo M, Caliaa A, Aiello MA (2013) Non-destructive techniques to assess mechanical and physical properties of soft calcarenitic stones. Proc Chem 8:35–44

    Google Scholar 

  19. 19.

    Breysse D (2012) Nondestructive evaluation of concrete strength: an historical review and a new perspective by combining NDT methods. Constr Build Mater 33:139–163

    Google Scholar 

  20. 20.

    Vasconcelos G, Lourenco PB, Alves CSA, Pamplona J (2007) Prediction of the mechanical properties of granites by ultrasonic pulse velocity and Schmidt hammer hardness. In: North American Masonry Conference, Missouri USA

  21. 21.

    Debailleux L (2018) Schmidt hammer rebound hardness tests for the characterization of ancient fired clay bricks. Int J Archit Herit 13(2):288–297

    Google Scholar 

  22. 22.

    Sbartai ZM, Laurens S, Elachachia SM, Payanc C (2012) Concrete properties evaluation by statistical fusion of NDT techniques. Constr Build Mater 37:943–950

    Google Scholar 

  23. 23.

    Ramos LF, Miranda TF, Mishra M, Fernandes FM, Manning E (2015) A Bayesian approach for NDT data fusion: the Saint Torcato Church case study. Eng Struct 84(1):120–129

    Google Scholar 

  24. 24.

    Mishra M (2013) A Bayesian approach for NDT data fusion. M.Sc. Thesis, University of Minho, Portugal

  25. 25.

    Kheder GF (1999) A two stage procedure for assessment of in situ concrete strength using combined non-destructive testing. Mater Struct 32:410–417

    Google Scholar 

  26. 26.

    Demirboga R, Turkmen R, Karakoc MB (2004) Relationship between ultrasonic velocity and compressive strength for high-volume mineral-admixtured concrete. Cem Concr Res 34(12):2329–2336

    Google Scholar 

  27. 27.

    Jain A, Kathuria A, Kumar A, Verma Y, Murari K (2013) Combined use of non-destructive tests for assessment of strength of concrete in structure. Proc Eng 54(2013):241–251

    Google Scholar 

  28. 28.

    Brozovsky J (2014) Determine the compressive strength of calcium silicate bricks by combined nondestructive method. Sci World J 2014:1–5

    Google Scholar 

  29. 29.

    Nobile L (2015) Prediction of concrete compressive strength by combined non-destructive methods. Meccanica 50(2):411–417

    Google Scholar 

  30. 30.

    Binda L, Fontana A, Frigerio G (1988) Mechanical behaviour of brick masonries derived from unit and mortar characteristics. In: Proceedings of the 8th international brick/block masonry conference Dublin, pp 205–16

  31. 31.

    Atkinson RH, Noland JL, Abrams DP (1982) A deformation theory for stack bonded masonry prisms in compression. In: Proceedings of 7th international brick masonry conference, Melbourne University, Melbourne pp 565–576

  32. 32.

    CEN (1998) EN 1052-1:1998 Methods for test for masonry—Part I: determination of compressive strength

  33. 33.

    ACI Committee 530 (1999) Building code requirements for masonry structure. American Concrete Institute, Farmington Hills

  34. 34.

    MSJC (2002) Masonry Standards Joint Committee, Building code requirements for masonry structures, ACI 530-02/ASCE 5-02/TMS 402-02, American Concrete Institute, Structural Engineering Institute of the American Society of Civil Engineers, The Masonry Society, Detroit

  35. 35.

    Mann W (1982) Statistical evaluation of tests on masonry by potential functions. In: Sixth international brick masonry conference

  36. 36.

    Hendry AW, Malek M (1986) Characteristic compressive strength of brickwork from collected test results. Mason Int 7:15–24

    Google Scholar 

  37. 37.

    Dayaratnam P (1987) Brick and reinforced brick structures. Oxford and IBH, New Delhi

    Google Scholar 

  38. 38.

    Bennett R, Boyd K, Flanagan R (1999) Compressive properties of structural clay tile prisms. J Struct Eng 123(7):920–926

    Google Scholar 

  39. 39.

    Kaushik HB, Rai DC, Jain SK (2007) Stress-strain characteristics of clay brick masonry under uniaxial compression. J Mater Civ Eng 19(9):728–739

    Google Scholar 

  40. 40.

    Ramamurthy K, Sathish V, Ambalavanan R (2000) Compressive strength prediction of hollow concrete block masonry prism. ACI Struct J 97(1):61–67

    Google Scholar 

  41. 41.

    Dymiotis C, Gutlederer BM (2007) Allowing for uncertainties in the modeling of masonry compressive strength. Constr Build Mater 16(7):1385–1393

    Google Scholar 

  42. 42.

    Gumaste KS, Rao KSN, Reddy BVV, Jagadish KS (2007) Strength and elasticity of brick masonry prisms and wallettes under compression. Mater Struct 40(2):241–253

    Google Scholar 

  43. 43.

    Costigan A, Pavía S, Kinnane O (2015) An experimental evaluation of prediction models for the mechanical behavior of unreinforced, lime-mortar masonry under compression. J Build Eng 4:283–294

    Google Scholar 

  44. 44.

    Trtnik G, Kavcic F, Turk G (2009) Prediction of concrete strength using ultrasonic pulse velocity and artificial neural networks. Ultrasonics 49:53–60

    Google Scholar 

  45. 45.

    Mishra M, Agarwal A, Maity D (2019) Neural-network-based approach to predict the deflection of plain, steel-reinforced, and bamboo-reinforced concrete beams from experimental data. SN Appl Sci 1:584. https://doi.org/10.1007/s42452-019-0622-1

    Article  Google Scholar 

  46. 46.

    Mashrei MA, Abdulrazzaq N, Abdalla TY, Rahmand MS (2010) Neural networks model and adaptive neuro-fuzzy inference system for predicting the moment capacity of ferrocement members. Eng Struct 32(6):1723–1734

    Google Scholar 

  47. 47.

    Zhou Q, Wang F, Zhu F (2016) Estimation of compressive strength of hollow concrete masonry prisms using artificial neural networks and adaptive neuro-fuzzy inference systems. Constr Build Mater 125:417–426

    Google Scholar 

  48. 48.

    Garzón-Roca J, Marco CO, Adam JM (2013) Compressive strength of masonry made of clay bricks and cement mortar: estimation based on neural networks and fuzzy logic. Eng Struct 48:21–27

    Google Scholar 

  49. 49.

    ud Darain AKM, Shamshirband S, Jumaat MZ, Obaydullah M (2015) Adaptive neuro fuzzy prediction of deflection and cracking behavior of NSM strengthened RC beams. Constr Build Mater 98:276–285

    Google Scholar 

  50. 50.

    Bilgeham M (2011) Comparison of ANFIS and NN models—with a study in critical buckling load estimation. Appl Soft Comput 11(4):3779–3791

    Google Scholar 

  51. 51.

    Zhu F, Wu Y (2014) A rapid structural damage detection method using integrated ANFIS and interval modeling technique. Appl Soft Comput 25:473–484

    Google Scholar 

  52. 52.

    Sobhani J, Najimi M, Pourkhorshidi AR, Parhizkar T (2010) Prediction of the compressive strength of no-slump concrete: a comparative study of regression, neural network and ANFIS models. Constr Build Mater 24(5):709–718

    Google Scholar 

  53. 53.

    Öztas̨ A, Pala M, Özbay E, Kanca E, C̨ağlar N, Bhatti MA (2006) Predicting the compressive strength and slump of high strength concrete using neural network. Constr Build Mater 20(9):769–775

    Google Scholar 

  54. 54.

    Madandoust R, Bungey JH, Ghavidel R (2012) Prediction of the concrete compressive strength by means of core testing using GMDH-type neural network and ANFIS models. Comput Mater Sci 51(1):261–272

    Google Scholar 

  55. 55.

    Yuan Z, Wang LN, Ji X (2014) Prediction of concrete compressive strength: research on hybrid models genetic based algorithms and ANFIS. Adv Eng Softw 67:156–163

    Google Scholar 

  56. 56.

    Khademi F, Jamal SM, Deshpande N, Londhe S (2016) Predicting strength of recycled aggregate concrete using artificial neural network, adaptive neuro-fuzzy inference system and multiple linear regression. Int J Sustain Built Environ 5(2):355–369

    Google Scholar 

  57. 57.

    Sadrmomtazi A, Sobhani J, Mirgozar MA (2013) Modeling compressive strength of EPS lightweight concrete using regression, neural network and ANFIS. Constr Build Mater 42:205–216

    Google Scholar 

  58. 58.

    Cüneyt Aydin A, Tortum A, Yavuz M (2006) Prediction of concrete elastic modulus using adaptive neuro-fuzzy inference system. Civ Eng Environ Syst 23(4):295–309

    Google Scholar 

  59. 59.

    Ahmadi-Nedushan B (2012) Prediction of elastic modulus of normal and high strength concrete using ANFIS and optimal nonlinear regression models. Constr Build Mater 36:665–673

    Google Scholar 

  60. 60.

    Duan ZH, Kou SC, Poon CS (2013) Using artificial neural networks for predicting the elastic modulus of recycled aggregate concrete. Constr Build Mater 44:524–532

    Google Scholar 

  61. 61.

    Bedirhanoglu I (2014) A practical neuro-fuzzy model for estimating modulus of elasticity of concrete. Struct Eng Mech 51(2):249–265

    Google Scholar 

  62. 62.

    Saridemir M (2009) Predicting the compressive strength of mortars containing metakaolin by artificial neural networks and fuzzy logic. Adv Eng Softw 40(9):920–927

    MATH  Google Scholar 

  63. 63.

    Singh R, Kainthola A, Singh TN (2012) Estimation of elastic constant of rocks using an ANFIS approach. Appl Soft Comput 12(1):40–45

    Google Scholar 

  64. 64.

    Marashi M, Torkashvand AM, Ahmadi A, Esfandyari M (2018) Adaptive neuro-fuzzy inference system: estimation of soil aggregates stability. Acta Ecol Sin 39(1):95–101

    Google Scholar 

  65. 65.

    Moayedi H, Hayati S (2018) Modelling and optimization of ultimate bearing capacity of strip footing near a slope by soft computing methods. Appl Soft Comput 66:208–219

    Google Scholar 

  66. 66.

    Esmaeili M, Osanloo M, Rashidinejad F, Bazzazi AA, Taji A (2014) Multiple regression, ANN and ANFIS models for prediction of backbreak in the open pit blasting. Eng Comput 30(4):549–558

    Google Scholar 

  67. 67.

    Ghasemi E, Kalhori H, Bagherpour R (2016) A new hybrid ANFIS-PSO model for prediction of peak particle velocity due to bench blasting. Eng Comput 32(4):607–614

    Google Scholar 

  68. 68.

    Jiang W, Arslan CA, Tehrani MS et al (2018) Simulating the peak particle velocity in rock blasting projects using a neuro-fuzzy inference system. Eng Comput 1:9. https://doi.org/10.1007/s00366-018-0659-6

    Article  Google Scholar 

  69. 69.

    Terzi S (2013) Modeling for pavement roughness using the ANFIS approach. Adv Eng Softw 57:59–64

    Google Scholar 

  70. 70.

    Orban Z, Gutermann M (2009) Assessment of masonry arch railway bridges using non-destructive in-situ testing methods. Eng Struct 31(10):228–2298

    Google Scholar 

  71. 71.

    Wu RT (2018) Data fusion approaches for structural health monitoring and system identification: past, present, and future. Struct Health Monit 1–35 https://doi.org/10.1177/1475921718798769

  72. 72.

    Bhatia AS (2018) Determination of compressive strength of the burnt clay brick mortar masonry structure (Unreinforced) using non-destructive experimental techniques. M. Tech thesis Indian Institute of Technology Kharagpur, 73 pages

  73. 73.

    Mishra M, Bhatia AS, Maity D (2019) Support vector machine for determining the compressive strength of brick-mortar masonry using NDT data fusion (case study: Kharagpur, India). Appl Sci 1(6):564. https://doi.org/10.1007/s42452-019-0590-5

    Article  Google Scholar 

  74. 74.

    Bureau of Indian Standard (BIS) 3495-1 TO 4 (1992) Methods of tests of burnt clay building bricks, pp 1–10

  75. 75.

    Bureau of Indian Standard (BIS) (1992) Common burnt clay building bricks. IS 1077:1992

  76. 76.

    Bureau of Indian Standard (BIS) (1999) Specification for sand for masonry mortars IS:2116-1980, 1980

  77. 77.

    RILEM, TC 127-MS MS. D.2 (1998) Determination of masonry rebound hardness. Mater Struct 31:375–377

    Google Scholar 

  78. 78.

    RILEM (1996) Measurement of ultrasonic pulse velocity for masonry units and walletttes, pp 467–469

  79. 79.

    Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw 5(6):989–993

    Google Scholar 

  80. 80.

    Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685

    Google Scholar 

  81. 81.

    Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modelling and control. IEEE Trans Syst 15:116–132

    MATH  Google Scholar 

  82. 82.

    Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    MATH  Google Scholar 

  83. 83.

    MATLAB (2010) Version 7.10.0 (R2010a) Natick. The MathWorks Inc., Massachusetts

Download references

Author information



Corresponding author

Correspondence to Mayank Mishra.

Ethics declarations

Conflict of interest

No potential conflict of interest is reported by the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (xlsx 11 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mishra, M., Bhatia, A.S. & Maity, D. A comparative study of regression, neural network and neuro-fuzzy inference system for determining the compressive strength of brick–mortar masonry by fusing nondestructive testing data. Engineering with Computers 37, 77–91 (2021). https://doi.org/10.1007/s00366-019-00810-4

Download citation


  • Neuro-fuzzy inference system
  • Brick masonry
  • Ultrasonic testing
  • Compressive strength
  • Non-destructive methods